In Ref. [1]} we have calculated the 5PN potential contributions to the Hamiltonian using
dimensional regularization in \(D = 4 - 2\varepsilon \)  space–time dimensions, including the pole terms and the
non–local contribution of the tail terms in complete form using harmonic coordinates.
The sum of these terms does still contain a pole contribution \(1/\varepsilon \) .
A canonical transformation leads to a pole–free Hamiltonian. In [1]} we have
left out finite rational 5PN terms of \(O(\nu ^2)\) , i.e. local tail contributions which are purely rational. We have
presented
already all the \(\pi ^2\)  terms of \(O(\nu ^2)\)  since they stem from the potential terms.
